Estimating alignment errors in sets of images

We describe a robust and accurate method for the estimation of alignment errors for sets of two-dimensional images, in the case where the true pattern is unknown. The intended application of the proposed method is cryoelectron microscopy, where two-dimensional views of individual proteins are observed in the electron microscope in random orientations and at modest SNR. By representing images in the basis of Fourier-harmonic (FH) coordinates and constructing averages and average intensities, we demonstrate that the variances of translation and rotational errors can be recovered.